Going by how many postcards have been sent from the countries, my rarest countries are:
Burundi:
Zambia:
Nigeria:
Palestine:
Nicaragua:
Guinea:
Those are the countries that have not yet sent 500 cards. Burundi only has 38, all sent by the receiver of my card, who no longer lives there. 
I’ve Just Sent A Card To Azerbaijan.
Bahamas
and
Trinidad and Tobago
Out of 950 sent cards the countries I have only sent one card to are: Chile, Cyprus, Greece, Israel, Jordan, Luxembourg, Mexico, North Macedonia, Slovakia, Trinidad and Tobago.
Yesterday I just got the address for someone in Qatar. I hope it arrives!
I guess my rarest country was Trinidad and Tobago I sent to last year
Yemen in both sent and received. At the moment there are no active users in Yemen, so I am pretty fortunate!
I’ve sent to Kazakhstan (and received from much rarer ones, like Panama) :
And one is on its way to a much rarer location, hopefully it’ll be registered ! 
Years ago I sent to Guam.
French Guiana
Namibia
Algeria is the rarest country for me
Has to be French Polynesia… only 20 members and only around 2500 cards received overall. Mine is still en route to Tahiti but it might take some time (looks like the average time it takes from UK to French Polynesia is around 141 days for that person 
).
Christmas Island 
I just received this one from French Guiana, which arrived remarkably quickly.
South Africa. Still traveling.
During my 9+ years in postcrossing I think these ones are the rariest:
Algeria:
ALAND ISLANDS. Has 38 members subscribed from the area!
Bangladesh
Uruguay
To French Polynesia.
